Explanation of the phase diagram of beta -di

Abstract

The organic superconductor \ensuremath{\beta}-di[bis(ethylenedithio)tetrathiafulvalene]triiodide, \ensuremath{\beta}-(BEDT-TTF${)}_{2}$${\mathrm{I}}_{3}$, shows an unusual phase diagram in temperature (T) and pressure (P) with large metastability domains for the stabilization of an incommensurate modulation. This behavior is related to the T-P cycling around a tricritical point. The superconducting properties are drastically affected by the nature of the structural ground state. In this paper, we present a simple microscopic mean-field model that satisfactorily explains the experimental phase diagram of \ensuremath{\beta}-(BEDT-TTF${)}_{2}$${\mathrm{I}}_{3}$. This model takes explicitly into account the two nonsymmetrical configurations of one of the two ethylene groups of the BEDT-TTF molecule, under the form of pseudospins linearly coupled to the vibrational degrees of freedom involved in the structural modulation. The calculations are performed as a function of the reduced interaction v=V/${k}_{B}$${T}_{c}$, where V is half the energy difference between the two ethylene group configurations and ${k}_{B}$${T}_{c}$ is the coupling energy between the vibrational degrees of freedom. The antiferrodistortive (commensurate) case is first treated; then the incommensurate case is solved. The phase diagram obtained as a function of v exhibits a tricritical point and large metastability domains. The experimental phase diagram is well accounted for by assuming a linear temperature and pressure dependence of V in the vicinity of the tricritical point. The origin of the incommensurate modulation of \ensuremath{\beta}-(BEDT-TTF${)}_{2}$${\mathrm{I}}_{3}$ is briefly discussed.